Range (mathematics)

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In mathematics, the range of a function is the set of all "output" values produced by that function. Sometimes it is called the image, or more precisely, the image of the domain of the function. Range is also occasionally used to indicate the difference between the largest and smallest numbers in a set of real-valued data.

Let the function f be a function on the real numbers:

f\colon \mathbb{R}\rightarrow\mathbb{R}

defined by

f(x) = x2.

The codomain of f is R, and f takes all nonnegative values but never takes negative values, and thus the range is in fact the set R+—non-negative reals, i.e. the interval [0,∞):

0\leq f(x)<\infty.

Now let g be a function on the real numbers:

g\colon \mathbb{R}\rightarrow\mathbb{R}

defined by

g(x) = 2x.

In this case the image of g equals R, its codomain, since, for any real number y,

g(y / 2) = y.

In other words, g is onto R.

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